(λa.(λb.λc.b)) and (λa.λb.λc.b)
I was wondering if someone could explain, using mostly English, what that lambda-calculus expression is supposed to mean, and whether there is any difference between the two given above.
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It's the same. In $λa.(λb.(λc.b))$ brackets are not mandatory because there is no other way to parse $λa.λb.λc.b$ with λ-calculus syntax: $$t ::= x \mid λx.t \mid t\,t$$ In English, your term is a function which returns a function which returns a function. It's roughly the same as a function which takes three arguments. Except that application must be done in three successive steps. (And in your case, the result is nothing more than the second argument.) |
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